Uniform rank metric stability of Lie algebras and groups

[2408.15614] Uniform rank metric stability of Lie algebras and groups Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Group Theory arXiv:2408.15614 (math) [Submitted on 28 Aug 2024 ( v1 ), last revised 15 Apr 2026 (this version, v2)] Title: Uniform rank metric stability of Lie algebras and groups Authors: Benjamin Bachner View a PDF of the paper titled Uniform rank metric stability of Lie algebras and groups, by Benjamin Bachner View PDF HTML (experimental) Abstract: We study uniform stability of discrete groups, Lie groups and Lie algebras in the rank metric, and the connections between uniform stability of these objects. We prove that semisimple Lie algebras are far from being flexibly $\mathbb{C}$-stable, and that semisimple Lie groups and lattices in semisimple Lie groups of higher rank are not strictly $\mathbb{C}$-stable. Furthermore, we prove that free groups are not uniformly flexibly $F$-stable over any field $F$. Comments: 24 pages Subjects: Group Theory (math.GR) Cite as: arXiv:2408.15614 [math.GR] (or arXiv:2408.15614v2 [math.GR] for this version) https://doi.org/10.48550/arXiv.2408.15614 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Benjamin Bachner [ view email ] [v1] Wed, 28 Aug 2024 08:13:19 UTC (26 KB) [v2] Wed, 15 Apr 2026 08:30:07 UTC (22 KB) Full-text links: Access Paper: View a PDF of the paper titled Uniform rank metric stability of Lie algebras and groups, by Benjamin Bachner View PDF HTML (experimental) TeX Source view license Current browse context: math.GR < prev | next > new | recent | 2024-08 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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